How can you write an equation of a line when you are given the slope and a point on the line? ACTIVITY: Writing Equations of Lines
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1 .7 Writing Equations in Point-Slope Form How can ou write an equation of a line when ou are given the slope and a point on the line? ACTIVITY: Writing Equations of Lines Work with a partner. Sketch the line that has the given slope and passes through the given point. Find the -intercept of the line. Write an equation of the line. a. m = b. m = COMMON CORE Writing Equations In this lesson, ou will write equations of lines using a slope and a point. write equations of lines using two points. Preparing for Standard 8.F. c. m = 7 d. m = 7 8 Chapter Graphing and Writing Linear Equations
2 ACTIVITY: Deriving an Equation Math Practice Construct Arguments How does a graph help ou derive an equation? Work with a partner. a. Draw a nonvertical line that passes through the point (,. b. Plot another point on our line. Label this point as (,. This point represents an other point on O the line. c. Label the rise and the run of the line through the points (, and (,. d. The rise can be written as. The run can be written as. Eplain wh this is true. e. Write an equation for the slope m of the line using the epressions from part (d. f. Multipl each side of the equation b the epression in the denominator. Write our result. What does this result represent? (, ACTIVITY: Writing an Equation Work with a partner. For months, ou saved $ a month. You now have $7 in our savings account. Draw a graph that shows the balance in our account after t months. Use our result from Activit to write an equation that represents the balance A after t months. Balance (dollars Savings Account A t Time (months. Redo Activit using the equation ou found in Activit. Compare the results. What do ou notice?. Wh do ou think = m( is called the point-slope form of the equation of a line? Wh do ou think it is important?. IN YOUR OWN WORDS How can ou write an equation of a line when ou are given the slope and a point on the line? Give an eample that is different from those in Activit. Use what ou learned about writing equations using a slope and a point to complete Eercises on page 88. Section.7 Writing Equations in Point-Slope Form 8
3 .7 Lesson Lesson Tutorials Ke Vocabular point-slope form, p. 8 Point-Slope Form Words A linear equation written in the form = m( is in point-slope form. The line passes through the point (,, and the slope of the line is m. slope (, Algebra = m( (, passes through (, O EXAMPLE Writing an Equation Using a Slope and a Point Write in point-slope form an equation of the line that passes through the point (, with slope. = m( Write the point-slope form. = [ ( ] Substitute for m, for, and for. = ( + Simplif. So, the equation is = ( +. Check Check that (, is a solution of the equation. = ( + Write the equation. =? ( + Substitute. 0 = 0 Simplif. Eercises Write in point-slope form an equation of the line that passes through the given point and has the given slope.. (, ; m =. (7, 0; m =. ( 8, ; m = 8 Chapter Graphing and Writing Linear Equations
4 Stud Tip EXAMPLE You can use either of the given points to write the equation of the line. Use m = and (,. ( = ( + = + 0 = + 8 Writing an Equation Using Two Points Write in slope-intercept form an equation of the line that passes through the points (, and (,. Find the slope: m = = = = Then use the slope m = and the point (, to write an equation of the line. = m( Write the point-slope form. = ( Substitute for m, for, and for. = + = + 8 Distributive Propert Write in slope-intercept form. EXAMPLE Real-Life Application You finish parasailing and are being pulled back to the boat. After seconds, ou are feet above the boat. (a Write and graph an equation that represents our height (in feet above the boat after seconds. (b At what height were ou parasailing? a. You are being pulled down at the rate of 0 feet per second. So, the slope is 0. You are feet above the boat after seconds. So, the line passes through (,. Use the point-slope form. = 0( Substitute for m,, and. 0 feet per second = = 0 + Distributive Propert Write in slope-intercept form. So, the equation is = 0 +. b. You start descending when = 0. The -intercept is. So, ou were parasailing at a height of feet (, 7 Eercises 7 Write in slope-intercept form an equation of the line that passes through the given points.. (,, (,. (,, (,. ( 8,, (, 9 7. WHAT IF? In Eample, ou are feet above the boat after seconds. Write and graph an equation that represents our height (in feet above the boat after seconds. Section.7 Writing Equations in Point-Slope Form 87
5 .7 Eercises Help with Homework. VOCABULARY From the equation = ( +, identif the slope and a point on the line.. WRITING Describe how to write an equation of a line using (a its slope and a point on the line and (b two points on the line. 9+(-= +(-= +(-9= 9+(-= Use the point-slope form to write an equation of the line with the given slope that passes through the given point.. m =. m =. m = Write in point-slope form an equation of the line that passes through the given point and has the given slope.. (, 0; m = 7. (, 8; m = 8. (, ; m = 9. (7, ; m = 7 0. (, ; m =. (, ; m = Write in slope-intercept form an equation of the line that passes through the given points.. (,, (,. (,, (,. (,, (, 7. (,, (8,. ( 9,, (, 7. (,, (, 8. CHEMISTRY At 0 C, the volume of a gas is liters. For each degree the temperature T (in degrees Celsius increases, the volume V (in liters of the gas increases b. Write an equation that represents the volume of the gas in terms of the temperature. 88 Chapter Graphing and Writing Linear Equations
6 9. CARS After it is purchased, the value of a new car decreases $000 each ear. After ears, the car is worth $8,000. a. Write an equation that represents the value V (in dollars of the car ears after it is purchased. b. What was the original value of the car? 0. REASONING Write an equation of a line that passes through the point (8, that is (a parallel and (b perpendicular to the graph of the equation =.. CRICKETS According to Dolbear s law, ou can predict the temperature T (in degrees Fahrenheit b counting the number of chirps made b a snow tree cricket in minute. For each rise in temperature of 0. F, the cricket makes an additional chirp each minute. a. A cricket chirps 0 times in minute when the temperature is 0 F. Write an equation that represents the temperature in terms of the number of chirps in minute. b. You count 00 chirps in minute. What is the temperature? c. The temperature is 9 F. How man chirps would ou epect the cricket to make? Leaning Tower of Pisa (0.7,. WATERING CAN You water the plants in our classroom at a constant rate. After seconds, our watering can contains 8 ounces of water. Fifteen seconds later, the can contains 8 ounces of water. a. Write an equation that represents the amount (in ounces of water in the can after seconds. b. How much water was in the can when ou started watering the plants? c. When is the watering can empt? 7.7 m. Problem Solving The Leaning Tower of Pisa in Ital was built between 7 and 0. a. Write an equation for the ellow line. b. The tower is meters tall. How far off center is the top of the tower? Graph the linear equation. (Section.. =. = +. = 7. MULTIPLE CHOICE What is the -intercept of the equation + = 0? (Section. A 0 B C D 0 Section.7 Writing Equations in Point-Slope Form 89
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